Dependence of the intrinsic line width of surface states on the wave vector: The Cu(111) and Ag(111) surfaces
The dependence of the intrinsic line width Γ of electron and hole states due to inelastic scattering on the wave vector k ∥ in the occupied surface state and the first image potential state on the Cu(111) and Ag(111) surfaces has been calculated using the GW approximation, which simulates the self-energy of the quasiparticles by the product of the Greens’s function and the dynamically screened Coulomb potential. Different contributions to the relaxation of electron and hole excitations have been analyzed. It has been demonstrated that, for both surfaces, the main channel of relaxation of holes in the occupied surface states is intraband scattering and that, for electrons in the image potential states, the interband transitions play a decisive role. A sharp decrease in the intrinsic line width of the hole state with an increase in k ∥ is caused by a decrease in the number of final states, whereas an increase in Γ of the image potential state is predominantly determined by an increase of its overlap with bulk states.
KeywordsFermi Level Surface State Line Width Relaxation Rate Image State
Unable to display preview. Download preview PDF.
- 17.G. Ferrini, C. Giannetti, D. Fausti, G. Galimberti, M. Peloi, G. Banfi, and F. Parmigiani, Phys. Rev. B: Condens. Matter 67, 235 407 (2003).Google Scholar
- 18.A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Fizmatgiz, Moscow, 1962; Pergamon, Oxford, 1965).Google Scholar
- 20.I. A. Nechaev, V. P. Zhukov, and E. V. Chulkov, Fiz. Tverd. Tela (St. Petersburg) 49(10), 1729 (2007) [Phys. Solid State 49 (10), 1811 (2007)].Google Scholar
- 28.G. Hörmandinger, Phys. Rev. B: Condens. Matter 49,13 897 (1994).Google Scholar
- 32.Th. Fauster and W. Steinmann, in Electromagnetic Waves: Recent Development in Research, Ed. by P. Halevi (Elsevier, Amsterdam, The Netherlands, 1995), Vol. 2, p. 350.Google Scholar
- 34.A. V. Chaplik, Zh. Éksp. Teor. Fiz. 60, 1845 (1971) [Sov. Phys. JETP 33, 997 (1971)].Google Scholar